Answer to Question #169950 in Statistics and Probability for Rustom

Question

Four coins are tossed. Let Y be the random variable representing the number of heads that occur. Find the values of the random variable Y.

Value of the Random Variable Y

Probability P(Y)

Answer 1

Let $X_i$ = 1, if head occur for coin i else 0, then $X_i$ is distributed according to Bernoulli distribution with parameter p = 0.5 (because coins are symmetrical)

Then $Y = \sum_{i=1}^4 X_i$ is distributed according to Binomial distribution with parameters p = 0.5 and n = 4.

Then possible values of Y: {0, 1, 2, 3, 4}

Probability distribution of Binomial distribution:

$Pr(Y=k) = C_n^k p^k (1-p)^{n-k} = \frac{4!}{(4-k)!k!}(\frac{1}{2})^4$

Pr(Y=0) = 0.0625

Pr(Y=1) = 0.25

Pr(Y=2) = 0.375

Pr(Y=3) = 0.25

Pr(Y=4) = 0.0625